Estimation of the Bulk Rock Density using Gravity Measurements

Underground Practical Course at TUBAF Himmelfahrt Fundgrube

2026-02-16

Task

  • Estimation of Gneiss block density
  • \(\rho \approx 2700\) kg/m\(^{-3}\)
  • Vertical difference of relative gravity readings taken at levels separated by \(\Delta h\)
  • Gravity meter Scintrex CG-5

Background

Real underground situation

  • Plate model not sufficient
  • Fill voids (shafts, galleries, etc.) with mass

💡 Gravity reductions

  • Shaft reduction \(\delta g_{S}\)
  • Gallery reduction \(\delta g_{G}\)
  • Cavity reduction \(\delta g_{C}\)
  • Terrain reduction \(\delta g_{T}\)

\[ \Delta g_{B} = \Delta g + \delta g_{S} + \delta g_{G} + \delta g_{C} + \delta g_{T} \]

\(\Delta g\): relative gravity, drift-corrected

\(\Delta g_{B}\): reduced relative gravity

Workflow

  • 4–5 students per group
  • Double-loop method, starting at base point P0
  • Clock-sync all readings
  • Depths tabulated

Further required for reductions:

  • Distance to shaft
  • Cross-section of gallery
  • Position relative to voids

Drift correction

Remove instrument drift taken at fixed point P0: \[ \Delta g(z) = g(z,t) - g_G(z_{0}, t), \]

The \(\Delta g(z)\) are the unreduced relative gravity data.

We now have to

  • fill the (known) underground voids, like shafts, galleries, cavities, etc.
  • remove the effect of topography above the mine

💡 \(\rightarrow\) Gravity reductions

Shaft reduction

  • Cross-section of shaft
  • Shaft bounded by P3 (top) and Rothschönberger Stolln (bottom)
  • Horizontal gravity meter position relative to the shaft

Cavity reduction

At P2 a cavity (Radstube) is right below the gravity meter. The missing rock mass has to be added to the plate model.

Terrain reduction

The terrain above the shaft is not flat. We approximate the piling by a rectangular prism of the same volume.

Numerical tools

We use Python to calculate the gravity effect of a rectangular 3-D prism.

gz = gz_prism(obs=(x, y, z), prism=(x1, x2, y1, y2, z1, z2), rho=2700)

Code is available at GitHub repository.

Report

Interval \(\Delta g_{2}\) [mGal] \(\Delta g_{1}\) [mGal] \(z_2 - z_1\) [m] \(g_h\) [mGal/m] \(\rho_B\) [kg/m³]
P0–P1
P1–P2
P2–P3
P0–P3

Report

Report

  • Assess the estimated density value
  • Discuss various reductions and their individual influence
  • Is there room for improvements?

Material

Python code, PDF’s, etc. are at https://github.com/TUBAF-EM/MineShaft_Geophysics